Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [lattice-surgery]

40 questions
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How does one modify the surface code cycle time in the code for "How to factor 2048 bit RSA integers with less than a million noisy qubits"?

The code in "How to factor 2048 bit RSA integers with less than a million noisy qubits" assumes a cycle time of 1 microsecond, which is too strict for neutral atoms. 1 millisecond sounds about right for neutral atoms. How much do the resources in…
Victory Omole
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Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)

In Litinsky's paper, there are many circuits relations, like the one below. The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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How to reason about absorbing Pauli Product rotations into measurements?

In this image, the orange box refers to the operator $\exp(-i P \frac{\pi}{4})$ and the blue box refers to the Pauli Measurement $P'$. The idea behind these rules is to show how all the Pauli Product $\frac{\pi}{4}$ rotations at the end of the…
shashvat
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How does one implement Hadamard gate in Pauli-based computation?

Pauli-based computation supposedly gives the full Clifford group. For instance, the CNOT can be implemented using joint ZZ measurement and joint XX measurement and using an additional ancilla qubit. To generate the Clifford group, it would be…
clearski
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How to measure the irregular stabilizers, as in "A Game of Surface Codes"?

I have been going through A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery; however, I am running into issues understanding the "irregular" stabilizers, first shown in figures 39 and 40. Specifically, I am confused by the…
buddhazapha
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What are the differences between code deformation, code conversion, code switching and gauge fixing?

From my understanding so far: Code switching is essentially just a fault-tolerant mapping between two codes. It's called code conversion if it's gradational, i.e. changes to stabilizer generators are measured in each round of error correction. A…
tomek
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When do we need to decode live the syndromes? Various examples to understand

I would like to precisely understand why we need to decode syndrome "live" when we want to perform $T$ gates. For this reason I consider different scenario (some are fictive but helpful to understand the physics) in order to understand which exact…
Marco Fellous-Asiani
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How to enumerate all low-weight undetectable logical errors from a stim circuit?

I have a stim.Circuit instance that is supposed to implement a distance 6 = 7 - 11 computation. It turns out that stim.Circuit.shortest_graphlike_error is able to find a undetectable weight-5 error (instead of the expected weight-6)2. But…
Adrien Suau
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Can you produce Non-Clifford gates via Lattice Surgery?

Is there any theorem stating that lattice merge/split operations (or perhaps more generally, so-called gauge-fixing) cannot produce a non-Clifford gate that can complete the universal gateset for the surface code?
usermm
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Lattice Surgery for Rectangular Surface Codes?

It has been shown that one can reduce the X or Z code distance for surface codes, when the noise is biased towards one type of fault. From my understanding, this is referred to as the rectangular surface code; where the main benefit is efficiency…
buddhazapha
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How does the expansion step for state injection in surface code lattice surgery work?

Looking at the oringal paper on lattice surgery on the surface code, the expansion step of the state injection process is meant to take $$\alpha|0\rangle_{L}+\beta|1\rangle_{L}$$ to a larger surface code patch. However, both this question and this…
GaussStrife
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Kraus decomposition of merging in lattice surgery

I am reading about lattice surgery from this paper. I am interested in the merge operation which takes 2 qubits to 1 qubit. I want to understand the logical-level Kraus operation that the merge does. For instance, the action of the rough merge…
qubit
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High logical error rates when implementing Lattice Surgery with Stim

I'm facing a strange issue with the logical error rate after implementing Lattice Surgery in Stim. For $d=3$ (I have some custom error annotations in the circuit), Logical error rate of X-basis Lattice Surgery, XX-Observable: 0.06361 Logical error…
control freak
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Number of logical cycles to implement $R_Z(\theta)$ gates in lattice surgery: why isn't it the number of layers $\times$ the $T$-count in $R_Z$?

Let's assume I want to implement a rotation $R_Z(\theta)$ for a lattice-surgery based computation, for $\theta$ being an arbitrary angle (i.e. the gate is not necessarily Clifford nor a $T$-gate). It can typically be done by Decomposing…
Marco Fellous-Asiani
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lattice surgery in state picture

I was following Surface code quantum computing by lattice surgery. A few questions about this paper have been asked in this forum, but I believe my question is new. The main text took a 'state picture' of what happens and in the appendix, the…
quTANum
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